Improving the speed of multi-way algorithms: Part I. Tucker3

Chemometrics and Intelligent Laboratory Systems

Volumn 42, Issue 1-2, 1998, Pages 93-103

  Andersson, Claus A ^a   Bro, Rasmus ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

3 MFA; Three mode factor analysis; Three way principal component analysis; Tucker3

Indexed keywords

ALGORITHM; ARTICLE; DATA ANALYSIS; PRIORITY JOURNAL; TIME;

EID: 0032563594     PISSN: 01697439     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0169-7439(98)00010-0     Document Type: Article

References (18)

1. [1] L. Tucker, Some mathematical notes on three-mode factor analysis, Psychometrika 31 (1966) 279-311.
2. [2] P.M. Kroonenberg, J. de Leeuw, Principal components analysis of three-mode data by means of alternating least squares algorithms, Psychometrika 45 (1980) 69-97.
3. [3] J.M.F. ten Berge, J. de Leeuw, P.M. Kroonenberg, Some additional results on principal components analysis of three-mode data by means of alternating least squares, Psychometrika 52 (1987) 183-191.
4. [4] C.L. de Ligny, M. Spanjer, J.C. van Houwelingen, H.M. Weesie, Three-mode factor analysis of data on retention in normal-phase high-performance liquid chromatography, J. Chromatogr. 301 (1984) 311-324.
5. [5] P.J. Gemperline, K.H. Miller, T. West, E. Weinstein, J.C. Hamilton, J.T. Bray, Principal component analysis, trace elements and blue crab shell disease, Anal. Chem. 64 (1992) 523-532.
6. [6] W.A. van der Kloot, P.M. Kroonenberg, External analysis with three-mode principal component analysis, Psychometrika 50 (1985) 479-494.
7. [7] A. Kapteyn, H. Neudecker, T. Wansbeek, An approach to n-mode components analysis, Psychometrika 91 (1986) 269-275.
8. [8] B.K. Alsberg, O.M. Kvalheim, Speed improvement of multivariate algorithms by the method of postponed basis matrix multiplications: Part I. Principal component analysis, Chemometr. Intell. Lab. Syst. 24 (1994) 31-42.
9. [9] B.K. Alsberg, O.M. Kvalheim, Speed improvement of multivariate algorithms by the method of postponed basis matrix multiplications: Part II. Three-mode principal component analysis, Chemometr. Intell. Lab. Syst. 24 (1994) 43-54.
10. [10] H. Kiers, R.A. Harshman, Relating two proposed methods for speedup of algorithms for fitting two-and three-way principal component and related multilinear methods, Chemometr. Intell. Lab. Syst. 39 (1997) 31-40.
11. [11] H.A.L. Kiers, P.M. Kroonenberg, J.M.T. ten Berge, An efficient algorithm for TUCKALS on data with large number of observation units, Psychometrika 33 (1992) 415-422.
12. [12] P.M. Kroonenberg, J.M.F. ten Berge, P. Brouwer, H. Kiers, Gram-Schmidt versus Bauer-Rutishauser in alternating least squares algorithms for three-mode principal component analysis, Comp. Stat. Q. 2 (1989) 81-87.
13. [13] H. Rutishauser, F.L. Computational aspects of, Bauer's simultaneous iteration method, Numer. Math. 13 (1969) 4-13.
14. [14] P.M. Kroonenberg, Three-mode principal component analysis, DSWO Press, Leiden, 1983.
15. [15] R. Bro, C.A. Andersson, Improving the speed of multi-way algorithms Part II: Compression, Chemometr. Intell. Lab. Syst. 42 (1998) 103-111.
16. [16] F.L. Bauer, Das Verfahren der Treppeniterationen und verwandte Verfahren zur Lösung algebraischer Eigenwertprobleme, ZAMP 8 (1957) 214-235.
17. [17] J.W. Longley, Least squares computations using orthogonalization methods, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, 1984.
18. [18] H.A.L. Kiers, Weighted least squares using ordinary least squares algorithms, Psychometrika 62 (1997) in press.